MarketWatch didn't say how the rumor started or who started it. But such a deal could be seen as a reaction to the new Apple Pay service announced last week. Through Apple Pay, iOS owners would be able to use their devices to purchase items from merchants who support the service. Google already has its Google Wallet service for mobile payments. But a stake in eBay (and its PayPal unit) could give the search giant more power in the payments market. Still, the rumor does seem shaky.

In an investor's note released early Monday, Piper Jaffray analyst Gene Munster expressed extreme doubt over such a deal, arguing that Google has a very limited history in buying chunks of public companies and that any interest in eBay's business would create a conflict of interest with other advertisers that use Google's search service.

"We believe that press reports circulating that Google is in talks with eBay to purchase a portion of the company are largely unsubstantiated and that it is unlikely that Google will purchase eBay," Munster said. "Speculation has ranged from vague to as specific as Google taking a 40 percent stake in eBay at $68/share (Reuters) [and] are conflicting and likely false."

Munster did throw out the idea of Google buying eBay's PayPal payments service but even that seems an "unlikely scenario," he said. eBay itself has so far resisted the idea of spinning off PayPal as a separate unit or to another company.

Further arguing his point, Munster said he didn't see any advantage to Google in owning a piece of eBay or PayPal. In light of the new Apple Pay service, Google might want to work more closely with eBay to integrate its service more heavily with Android. But an ownership of eBay isn't necessary for that to happen, the analyst said.

And if Google were interested in diving further into the mobile payments arena, the company could do more to push and promote its Google Wallet product, which so far has failed to catch on with consumers.

"In fact, we believe that if Google intends to be a significant player as a mobile wallet provider, it might be better served spending a much smaller portion of what they could buy a 40 percent stake in eBay for to market Google Wallet and incentivize consumers to use it," Munster said. "Lastly we believe that if Google were to take full ownership of PayPal that it may restrict PayPal's ability to be incorporated into Apple Pay or cause other competitive turmoil."

Is there any scenario under which Google could acquire PayPal? Munster maps out a potential case but still doesn't see such a deal as viable:

Given the Apple Pay announcement and the incorporation of NFC into the newest iPhone, we believe that mobile payments are prepared to take a major step forward -- Google has an economic incentive to stay relevant in mobile payments and may be looking to secure its position in the transition phase. Under Google, PayPal would be exposed to massive amounts of data it could use to further mitigate risk and could flourish much faster than it has under eBay's cost-conscious model...The bottom line is that PayPal alone could be worth $62 billion or potentially more to a suitor like Google (requiring Google to likely raise debt or do a secondary), but we find it hard to see a scenario where the companies come to an agreement that appeases both sides.